Perturbation Theory for Open Two-Level Nonlinear Quantum Systems

Perturbation theory is an important tool in quantum mechanics. In this paper, we extend the traditional perturbation theory to open nonlinear two-level systems, treating decoherence parameterγ as a perturbation. By this virtue, we give a perturbative solution to the master equation, which describes a nonlinear open quantum system. The results show that for small decoherence rateγ, the ratio of the nonlinear rate C to the tunneling coefficient V (i.e., r=C/V) determines the validity of the perturbation theory. For small ratio r, the perturbation theory is valid, otherwise it yields wrong results.     

三苯基咔咯金属配合物的振动光谱和DFT计算

对三苯基咔咯金属配合物(MTPC, M=Ni, Cu, Co, Mn)的拉曼和红外光谱进行了实验研究. 用DFT方法计算了其基态几何结构以及红外和拉曼光谱,并基于计算结果对测量到的振动谱带进行了局域坐标归属. 研究发现,由于对称性降低,咔咯金属配合物的振动光谱比卟啉金属配合物更为复杂,若干咔咯骨架振动与苯取代基强烈耦合.考察了拉曼和红外谱带频率变化与咔咯环结构的关系,发现随着环内核尺寸的减小,与C^I_αC^I_α键伸缩振动和C?Cm键伸缩振动相关的拉曼谱带频率增加,其中C^I_αC^I_α伸缩振动的拉曼谱带对环内核尺寸的变化更为敏感且呈良好的线性关系,可以作为反映金属咔咯骨架结构变化的特征谱带.     

Nonlinear Quantum Mechanics at the Planck Scale

I argue that the linearity of quantum mechanics is an emergent feature at the Planck scale, along with the manifold structure of space-time. In this regime the usual causality violation objections to nonlinearity do not apply, and nonlinear effects can be of comparable magnitude to the linear ones and still be highly suppressed at low energies. This can offer alternative approaches to quantum gravity and to the evolution of the early universe. PACS: 04.60.-m, 03.65.Ta     

Quantum theory of nonlinear processes

Principles of development of the quantum theory of nonlinear processes on the basis of Lagrangian formulation are discussed. It is shown that in the framework of this formulation it is possible to preserve succession from the classical theory and, in particular, use these methods for studies of quantum systems. The quantum dispersion of a nonlinear oscillator excited by an external source and of a parametric generator is calculated. Its role is established in the solution of the problem of stability of oscillations.     

空间周期磁场中单电子量子点的能谱和磁化强度

研究了在空间周期磁场下,单电子量子点中电子的能谱和基态磁化强度,并对它们随周期磁场的各个参数(B、β、ψ)的变化作了分析.在计算中使用GaAs量子点模型,同时把二维各向同性谐振子的本征态作为基矢.计算发现,β对量子点的影响最大,β较小时,能谱和基态磁化强度与均匀磁场中的结果相似,反之则差别很大.在随β变化的能谱图中,大B较之小B表现出更丰富的谱线信息.当β足够大时,周期磁场对量子点的影响几乎为零.在计算中β越大,则所需的基的最少个数越多,否则计算结果不准确.     

四-(叔丁基)-四氮杂卟啉金属配合物的振动光谱和DFT计算

测量了四-(叔丁基)-四氮杂卟啉金属配合物(MT(tBu)TAP,M=Cu, Co, Ni, Zn)的拉曼和红外光谱. 在B3LYP理论水平上计算了其基态结构和振动光谱,基于计算结果对观察到的拉曼谱带进行了详细的指认. 考察了拉曼和红外谱带频率变化与四氮杂卟啉环结构的关系. 随着环内核尺寸的减小,C_βC_β′伸缩振动(A_g)、C_αN_m反对称伸缩振动(A_g)、以及C_αN_m对称伸缩振动(B_g) 的频率线性地增加,其中后两者对环内核尺寸的变化更为敏感.     

Quantum Set Theory

The complete orthomodular lattice of closed subspaces of a Hilbert space is considered as the logic describing a quantum physical system, and called a quantum logic. G. Takeuti developed a quantum set theory based on the quantum logic. He showed that the real numbers defined in the quantum set theory represent observables in quantum physics. We formulate the quantum set theory by introducing a strong implication corresponding to the lattice order, and represent the basic concepts of quantum physics such as propositions, symmetries, and states in the quantum set theory.     

Quantum Fisher Information Gap for Systems with Nonlinear Hamiltonians

Quantum Fisher information(QFI) gap characterizes the stability of QFI to space directions. We study the QFI distributions and QFI gap for quantum states generated from nonlinear Hamiltonians for both spin and bosonic systems. We find that the same spin-squeezing parameter(or principle squeezing parameter) corresponds to two different values QFI gap, and the locations of all extreme points of the QFI are explicitly given.     

Free-Fall Non-Universality in Quantum Theory

The author shows by embodying the Einstein equivalence principle—local Poincaré invariance—and general covariance in quantum theory that wave-function spreading rules out the universality of free fall, that is, the free-fall trajectory of a quantum (test) particle depends on its internal properties. The author provides a quantitative estimate of the free-fall non-universality in terms of the Eötvös parameter, which turns out to be measurable in atom interferometry.     

Anthropic Interpretation of Quantum Theory

The problem of interpreting quantum theory on a large (e.g. cosmological) scale has been commonly conceived as a search for objective reality in a framework that is fundamentally probabilistic. The Everett programme attempts to evade the issue by the reintroduction of determinism at the global level of a state vector of the universe. The present approach is based on the recognition that, like determinism, objective reality is an unrealistic objective. It is shown how an objective theory of an essentially subjective reality can be set up using an appropriately weighted probability measure on the relevant set of Hilbert subspaces. It is suggested that an entropy principle (superseding the weak anthropic principle) should be used to provide the weighting that is needed. The application of this ansatz to a toy gedanken example (involving Schroedinger's legendary cat) is described in an appendix.     

Effective Field Theory of Random Quantum Circuits

Quantum circuits have been widely used as a platform to simulate generic quantum many-body systems. In particular, random quantum circuits provide a means to probe universal features of many-body quantum chaos and ergodicity. Some such features have already been experimentally demonstrated in noisy intermediate-scale quantum (NISQ) devices. On the theory side, properties of random quantum circuits have been studied on a case-by-case basis and for certain specific systems, and a hallmark of quantum chaos—universal Wigner–Dyson level statistics—has been derived. This work develops an effective field theory for a large class of random quantum circuits. The theory has the form of a replica sigma model and is similar to the low-energy approach to diffusion in disordered systems. The method is used to explicitly derive the universal random matrix behavior of a large family of random circuits. In particular, we rederive the Wigner–Dyson spectral statistics of the brickwork circuit model by Chan, De Luca, and Chalker [Phys. Rev. X 8, 041019 (2018)] and show within the same calculation that its various permutations and higher-dimensional generalizations preserve the universal level statistics. Finally, we use the replica sigma model framework to rederive the Weingarten calculus, which is a method of evaluating integrals of polynomials of matrix elements with respect to the Haar measure over compact groups and has many applications in the study of quantum circuits. The effective field theory derived here provides both a method to quantitatively characterize the quantum dynamics of random Floquet systems (e.g., calculating operator and entanglement spreading) and a path to understanding the general fundamental mechanism behind quantum chaos and thermalization in these systems.     

Quantum Theory from Four of Hardy's Axioms

In a recent paper [e-print quant-ph/0101012], Hardy has given a derivation of quantum theory from five reasonable axioms. Here we show that Hardy's first axiom, which identifies probability with limiting frequency in an ensemble, is not necessary for his derivation. By reformulating Hardy's assumptions, and modifying a part of his proof, in terms of Bayesian probabilities, we show that his work can be easily reconciled with a Bayesian interpretation of quantum probability.     

瞬态光谱量子分析及其测量

介绍了新近研制的瞬态光谱测量仪，详细分析了瞬态光谱测量中的量子转换过程，进而表述出瞬态光谱信噪比表达式、图像参数和光电转换量子效率、光电成像有效积分时间和CCD光敏面的作用，最后给出了在此理论指导下的实测光谱曲线。     

电荷不连续时电容耦合介观电路的量子回路方程及其能谱

考虑电荷具有不连续性的事实对双LC介观电路进行量子化,给出耦合形式的量子回路方程以及无相互作用Hamilton本征基矢下的电路能谱.结果表明,计及电荷离散性将使回路方程的形式发生明显变化;介观电路的能谱除与电路参数相关外,还明显地依赖于电荷的量子化性质.     

Quantum Computation with Nonlinear Optics

We propose a scheme of quantum computation with nonlinear quantum optics. Polarization states of photons are used for qubits. Photons with different frequencies represent different qubits. Single qubit rotation operation is implemented through optical elements like the Faraday polarization rotator. Photons are separated into different optical paths, or merged into a single optical path using dichromatic mirrors. The controlled-NOT gate between two qubits is implemented by the proper combination of parametric up and down conversions. This scheme has the following features： （1） No auxiliary qubits are required in the controlled-NOT gate operation; （2） No measurement is required in the course of the computation; （3） It is resource efficient and conceptually simple.     

Characterizing Quantum Theory in Terms of Information-Theoretic Constraints

We show that three fundamental information-theoretic constraints—the impossibility of superluminal information transfer between two physical systems by performing measurements on one of them, the impossibility of broadcasting the information contained in an unknown physical state, and the impossibility of unconditionally secure bit commitment—suffice to entail that the observables and state space of a physical theory are quantum-mechanical. We demonstrate the converse derivation in part, and consider the implications of alternative answers to a remaining open question about nonlocality and bit commitment.